While Romney still holds the lead at 27 percent in the poll, Huckabee comes in a strong second at 21 percent, with a 5 percent margin of error.
The poll also shows that Democrats are headed toward a heated showdown in Iowa, where holds a statistically insignificant lead over and .
Among likely caucus-goers, Clinton came out on top with 25 percent support, but she was trailed closely by Edwards at 23 percent, and Obama at 22 percent. With a margin of error of 4 percentage points, there is no clear leader. Trailing behind was , at 12 percent, with all other candidates in single digits.
The situation in Iowa, where nominating caucuses are scheduled for Jan. 3, is in stark contrast to New Hampshire, where Clinton and Romney continue to hold large leads among those likely to vote in the state's first-in-the-nation primary, which could come only days after Iowa's contests.
But in both states, large chunks of voters have yet to make up their minds, meaning the results of the contests that will kick off the 2008 nominating season are still difficult to predict.
In the poll, was in third in Iowa at 15 percent. All other candidates were in single digits, including , who had 9 percent support among likely caucus-goers.
While Huckabee's strong showing would seem to be a surprise, CBSNews.com senior political editor Vaughn Ververs said it's the attention he's paid to the state coupled with his conservative message that is paying dividends.
"A poll, of course, is simply a snapshot in time and we'll need to see more evidence of a Huckabee surge before buying into it totally," "But it's not surprising to see him gaining. Iowa is a state tailor made for Huckabee's candidacy and message." (Read more in CBSNews.com's campaign blog, Horserace)
"Huckabee is a very good candidate in the sense he makes a very good appearance," CBS News chief Washington correspondent Bob Schieffer said. "I think that Huckabee actually has a chance to win out there… If he does, that puts a whole new spin on the race."
"I'm still not sure he would be the favorite to get the nomination, but he's certainly going to be a factor as we move on down the road," Schieffer added.
While Romney still has the lead in Iowa, his support base is softer than that of Huckabee, a former Arkansas governor whose campaign has gained momentum in recent weeks. Half of Huckabee supporters said they had made up their mind, compared to two-thirds of Romney supporters who said they could change their mind before caucus night. Overall, 57 percent of GOP caucus-goers said they haven't settled on one candidate.
Huckabee could run into trouble if immigration is as important an issue as the poll indicates. When asked what issue candidates should discuss, illegal immigration topped the list at 20 percent, and 44 percent of caucus-goers said illegal immigrants should lose their jobs and leave the country. Huckabee has been criticized for supporting pre-natal care for immigrants and educational opportunities for the children of immigrants, and only 13 percent said Huckabee agreed with them on this issue, compared to 26 percent for Romney.
However, immigration may not be a deal-breaker: 75 percent said they could support a candidate who is less conservative than they are. This could offer hope to Huckabee, but not to Giuliani. While 38 percent said he was the most electable of the GOP candidates, likely caucus-goers were split nearly evenly on whether they could support a candidate who disagreed with them on social issues like abortion and gay marriage - Giuliani favors abortion rights and supports extending gay rights, though he does not support same-sex marriage.